Geometric ℓ<inf>p</inf>-norm feature pooling for image classification

Abstract

Modern visual classification models generally include a feature pooling step, which aggregates local features over the region of interest into a statistic through a certain spatial pooling operation. Two commonly used operations are the average and max poolings. However, recent theoretical analysis has indicated that neither of these two pooling techniques may be qualified to be optimal. Besides, we further reveal in this work that more severe limitations of these two pooling methods are from the unrecoverable loss of the spatial information during the statistical summarization and the underlying over-simplified assumption about the feature distribution. We aim to address these inherent issues in this work and generalize previous pooling methods as follows. We define a weighted ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -norm spatial pooling function tailored for the class-specific feature spatial distribution. Moreover, a sensible prior for the feature spatial correlation is incorporated. Optimizing such pooling function towards optimal class separability yields a so-called geometric ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -norm pooling (GLP) method. The described GLP method is capable of preserving the class-specific spatial/geometric information in the pooled features and significantly boosts the discriminating capability of the resultant features for image classification. Comprehensive evaluations on several image benchmarks demonstrate that the proposed GLP method can boost the image classification performance with a single type of feature to outperform or be comparable with the state-of-the-arts.